Lorenzo Catani

Chapman University · Department of Physics and Computational Science

In this work we present a hierarchy of generalized contextuality. It refines the traditional binary distinction between contextual and noncontextual theories, and facilitates their comparison based on how contextual they are. Our approach focuses on the contextuality of prepare-and-measure scenarios, described by general probabilistic theories (GPT...

In this paper we relate notions of nonclassicality in what is known as the simplest nontrivial scenario (a prepare and measure scenario composed of four preparations and two binary-outcome tomographically complete measurements). Specifically, we relate the established method developed by Pusey [M. F. Pusey, Phys. Rev. A 98, 022112 (2018)] to witnes...

In this work we focus on two classes of games: xor nonlocal games and xor* sequential games with monopartite resources. xor games have been widely studied in the literature of nonlocal games, and we introduce xor* games as their natural counterpart within the class of games where a resource system is subjected to a sequence of controlled operations...

Quantum interference phenomena are widely viewed as posing a challenge to the classical worldview. Feynman even went so far as to proclaim that they are the only mystery and the basic peculiarity of quantum mechanics. Many have also argued that basic interference phenomena force us to accept a number of radical interpretational conclusions, includi...

Interference phenomena are often claimed to resist classical explanation. However, such claims are undermined by the fact that the specific aspects of the phenomenology upon which they are based can in fact be reproduced in a noncontextual ontological model [Catani et al., arXiv:2111.13727]. This raises the question of what other aspects of the phe...

In the framework of ontological models, the inherently nonclassical features of quantum theory always seem to involve properties that are fine tuned, i.e. properties that hold at the operational level but break at the ontological level. Their appearance at the operational level is due to unexplained special choices of the ontological parameters, wh...

We investigate the relationship between two properties of quantum transformations often studied in popular subtheories of quantum theory: covariance of the Wigner representation of the theory and the existence of a transformation noncontextual ontological model of the theory. We consider subtheories of quantum theory specified by a set of states, m...

Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered to be a way in which it entails a departure from the classical worldview. However, this perspective is underm...

Interference phenomena are often claimed to resist classical explanation. However, such claims are undermined by the fact that the specific aspects of the phenomenology upon which they are based can in fact be reproduced in a noncontextual ontological model [Catani et al. arXiv:2111.13727]. This raises the question of what other aspects of the phen...

In this work we focus on two classes of games: XOR nonlocal games and XOR* sequential games with monopartite resources. XOR games have been widely studied in the literature of nonlocal games, and we introduce XOR* games as their natural counterpart within the class of games where a resource system is subjected to a sequence of controlled operations...

Our article [arXiv:2111.13727(2021)] argues that the phenomenology of interference that is traditionally regarded as problematic does not, in fact, capture the essence of quantum theory -- contrary to the claims of Feynman and many others. It does so by demonstrating the existence of a physical theory, which we term the "toy field theory", that rep...

Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered to be a way in which it entails a departure from the classical worldview. However, this view is undermined by...

We connect two key concepts in quantum information: compatibility and divisibility of quantum channels. Two channels are compatible if they can be both obtained via marginalization from a third channel. A channel divides another channel if it reproduces its action by sequential composition with a third channel. (In)compatibility is of central impor...

Quantum interference phenomena are widely viewed as posing a challenge to the classical worldview. Feynman even went so far as to proclaim that they are the only mystery and the basic peculiarity of quantum mechanics. Many have also argued that such phenomena force us to accept a number of radical interpretational conclusions, including: that a pho...

We relate two notions of classicality for quantum transformations often arising in popular subtheories of quantum mechanics: covariance of the Wigner representation of the theory and the existence of a transformation noncontextual ontological model of the theory. We show that covariance implies transformation noncontextuality. The converse holds pr...

In the framework of ontological models, the features of quantum mechanics that emerge as inherently nonclassical always involve properties that are fine tuned, i.e. properties that hold at the operational level but break at the ontological level (they only hold for fine tuned values of the ontic parameters). Famous examples of such features are con...

Spekkens’ toy model (SM) is a non-contextual hidden-variable model made to support the epistemic view of quantum theory, where quantum states are states of partial knowledge about a deeper underlying reality. Despite being a classical model, it has reproduced many features of quantum theory (entanglement, teleportation, . . .): (almost) everything...

We introduce a simple single-system game inspired by the Clauser-Horne-Shimony-Holt (CHSH) game. For qubit systems subjected to unitary gates and projective measurements, we prove that any strategy in our game can be mapped to a strategy in the CHSH game, which implies that Tsirelson's bound also holds in our setting. More generally, we show that t...

One of the main questions in the field of quantum computation is where the quantum computational speed-up comes from. Recent studies in the field of quantum foundations have suggested which are the features to be considered as inherently non-classical. One of the major contributions in this direction comes from a result known as Spekkens' toy theor...

We introduce a simple single-system game inspired by the Clauser-Horne-Shimony-Holt (CHSH) game. For qubit systems subjected to unitary gates and projective measurements, we prove that any strategy in our game can be mapped to a strategy in the CHSH game, which implies that Tsirelson's bound also holds in our setting. More generally, we show that t...

Spekkens' toy theory is a non-contextual hidden variable model with an epistemic restriction, a constraint on what the observer can know about the reality. It has been shown in [3] that for qudits of odd dimensions it is operationally equivalent to stabiliser quantum mechanics by making use of Gross' theory of discrete Wigner functions. This result...

Spekkens' toy model is a non-contextual hidden variable model with an epistemic restriction, a constraint on what an observer can know about reality. The aim of the model, developed for continuous and discrete prime degrees of freedom, is to advocate the epistemic view of quantum theory, where quantum states are states of incomplete knowledge about...